10:00 AM-12:00 PM
Room: Wasatch A/B
In the past decade, a great deal of progress was made in using dynamical systems and solitons to studying the dynamics of nonlinear partial differential equations. Many applications, such as nonlinear optics, furnish examples that exhibit both very regular and chaotic dynamics. There has, therefore, always existed a beneficial mutual interaction between these fields and various branches of dynamical systems, including, more recently, those pertaining to partial differential equations. The speakers in this minisymposium will illustrate this interaction by describing the dynamical behavior of specific partial differential equations that arise in nonlinear optics and other applied fields, and discussing several new techniques. These include dynamical systems analysis of homoclinic orbits and chaotic dynamics in partial differential equations, turbulence theory, kinetic equations, numerical computations and diagnostics for nonlinear partial differential equations, and perturbation theory for near-integrable partial differential equations and solitons. Applications will include semiconductor lasers, long ring-cavity gas lasers, and fiber optics. Analytical and numerical studies will be presented.
Organizers: Gregor Kovacic
Rensselaer Polytechnic Institute
LMH, 1/8/99; tjf, 2/2/99